Notes on thermodynamics of super-entropic AdS black holes

TL;DR

This paper derives new thermodynamic relations for super-entropic AdS black holes, showing they can be obtained from conventional black holes via the ultra-spinning limit, and extends these relations across various dimensions and black hole types.

Contribution

It introduces a new mass formula for super-entropic black holes and establishes simple relations linking their thermodynamics to conventional black holes.

Findings

Thermodynamic quantities of super-entropic black holes can be derived from standard black holes using the ultra-spinning limit.

Derived a Christodoulou-Ruffini-like squared-mass formula for super-entropic Kerr-Newman-AdS black holes.

Extended the thermodynamic relations to higher dimensions and other black hole configurations.

Abstract

The super-entropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS super-entropic black hole, and then establish a set of very simple relations between thermodynamic quantities of the super-entropic Kerr-Newman-AdS$_4$ black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS$_4$ super-entropic black hole can be obtained from those of the usual pro-type by taking the ultra-spinning limit properly. Then these relations are extended to the singly-rotating Kerr-AdS black holes in arbitrary dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged supergravity. It can be inferred that the thermodynamic quantities of all super-entropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes, and thus can be obtained by taking the ultra-spinning limit appropriately.